the subset of simple stable curves (see [1]}), and similarly \(\mathcal {M}^*_\Gamma (J) \subset \mathcal {M}_\Gamma (J)\) , \(\widetilde{\mathcal {M}}^*_\Gamma (J)\subset \widetilde{\mathcal {M}}_\Gamma (J)\) , and \(\mathcal {M}^*(\Gamma ,J) \subset \mathcal {M}(\Gamma ,J)\) .
Explicitly, the latter is the subset of tuples \(\mathbf {u}\)  such that \(u_\alpha (\mathbb {CP}^1) \ne u_\beta (\mathbb {CP}^1)\)  for \(\alpha \ne \beta \)  such that \(u_\alpha \)  and \(u_\beta \)  are non-constant, and non-constant \(u_\alpha \)  are simple.
